Example: "Basically the paper is so horribly written that it’s impossible to read it without AI help. I asked Astra for reasonable completeness and soundness claims of the noise gadget and it gave them by combining claims from all over the paper."
Without AI help? Impossible. With AI help? Comprehensible.
That is consistent with the assertion that mathematics might outlast human mathematicians.
(Feels related to models evolving forms of human-incomprehensible shorthand when communicating among themselves.)
Without making a value judgement of whether that's good or bad for the field in the long term, it is an interesting point to note the similarity with the human-incomprehensible communication among AI agents. When there are no humans in the loop, it's no longer necessary to translate or "lower" the representation for our benefit. Since it's still early days, we can only imagine and extrapolate how far it might go in that direction, what might evolve out of it in the future.
Incomprehensible pure mathematics has no value to anyone.
It's not a given that mathematics will survive without mathematicians. It's not even likely. The proofs OpenAI threw over the wall are unpublishable garbage, top to bottom. A big reason mathematicians are so upset is that they feel like they've been drafted into the role of unpaid editor for OpenAI.
Make no mistake about it, the mathematical profession is under attack. The biggest incentive for becoming a mathematician (as opposed to a hired gun quant) is the challenge of solving the proofs. Take that away and the most talented problem solvers go with it.
In time, the profession of mathematics will evolve so a new task is at the center of the diagram--maybe it will be explaining math results to humans or teaching math to future mathematicians.
That is the centre of mathematics. It's what schools pay mathematicians to do. All the research stuff, the problem solving, the "thrill of the hunt" for elusive proofs, and the prestige of being the first? That's the carrot the schools dangle in front of mathematicians' noses to get them to work. Without that, you don't get exceptional mathematicians teaching classes and supervising grad students (and attracting the world's top students to your school); you get adjuncts and only adjuncts.